Finite Group Databasebeta

C22×(C2×D431)⋊C4 #42119506

order27584
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D431)⋊C4

Splittings

FittingC23×C4×C431 ⋊ C2
SylowC431 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D431
commutatorC2×C431C23×C4
FrattiniC22C23×D431
FittingC23×C4×C431C2
socleC24×C431C22
prime radicalC24×D431C2
cosocleC22×C431C24
hypercenterC23×C4D431
hypocenterC431C22×C22⋊C4
LCSG ▷ C2×C431 ▷ C431
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13792

Conjugacy classes & character table

6920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27584, 996);